 I'm a senior research specialist at the Department of Medical, Epidemiology and Biostatistics at Caroline's Institute in Stockholm, Sweden. Today I'm going to give you a talk about meta-analysis of dose-response studies with the dose-response meta-r package that I wrote, and this is going to be the outline for the talk today. I'm going to present this as a vignette of the dose-response meta-package. I will cover the very basic idea or rationale behind the dose-response meta-analysis. I will talk a little bit about the aggregated dose-response data with a practical example, and then I will cover the two different phases of the analysis. So the dose-response analysis for a single study, and then how to perform this same analysis where we have multiple studies. I will cover the main feature of the dose-response meta-package as originally thought in the first implementation, and I will also talk about some of the model extensions that have been recently implemented, and I will conclude with some references and codes. So what is dose-response meta-analysis? Dose-response meta-analysis is a technique, an analysis, where we want to derive a dose-response curve from results that have been published on different journals or on different resources, and these results try to summarize the association between a quantitative exposure. So we are talking about, for example, number of cigarettes. We are going to see how we are going to use a number of cups of coffee per day, and then we want to relate this exposure to the currents of a health outcome or some other outcome. We will focus on mortality risk or some other example, it could be incidence of a disease. So the research question that we can address with this methodology is to evaluate if there is an association between the exposure and the outcome, and what is in particular the shape of this exposure, and in such a way we can define also which are or try to identify those exposure intervals or doses which are associated with the best or worst diagnosis on the outcome, and then we can also try to identify those factors that may explain differences in the association. We are going to see some examples later on. But just to give you a little bit the idea of the importance of this technique, it has very different field of application. Many of those responses are currently published in leading medical and epidemiological journal, and they are also used frequently by international health organizations and academic institutions. So many of the measures that are currently reported by public health agencies are actually based on this meta-analysis. Let's have a look on the aggregated data that are the basis of this meta-analysis, and we are going to do this by using, as a motivating example, one of those response meta-analysis that I have been published in the last year, and this is about modeling the association between the coffee consumption and different health outcomes. In particular, all-cause mortality, cardiovascular mortality, and then cancer mortality. We're going to use all-cause mortality in this example. So I'm going to put some of the code, so you can also reproduce the results in these slides. We're going to see, for example, how this, by loading the DOSOLES meta-R package, the data are included in the coffee mortality object, and you see a little bit the structure of the data. We have two different studies that report D as a measure of association to log relative risk with the corresponding standard error for different doses of coffee consumption, and they use one of the first doses as a reference. And they then compare increasing doses, how the log relative risk changes for increasing doses of coffee compared to the reference one. So we can see how we can run those response analysis based just on one study, and we're going to use, I'm just going to present some descriptives of the studies. So here we see the study by Legredi in 1987, and we see how using half a cup of coffee per day as a reference, we see a slow decrease in the risk, or in the mortality risk, or increases doses, and this reduction then disappear and higher doses. So the key feature here is that all these points are not independent, because they are based as a relative comparison using the first group as a reference, and then because of this, the relative risk in the relevant group is equal to zero, or to one, or the log of this one number equal to zero by definition. So what we're going to do is we're going to relate, run a linear model, actually a log linear model, where we have this outcome, the log relative risk on the non-referring doses, and then we have a design matrix where it's going to specify how we're going to model our relationship. And again the model is without an intercept, because by definition the relative risk is equal to one on the reference dose, and then we can estimate or approximate the covariance of the residuals using additional information. So depending on the study design, then we can use the information about the number of cases or controls, or for core studies about the number of participants and the person times accumulated to estimate this covariance. And here we can use the covar log rr function to exactly do this, if we're interested in having a look at that quantity. And then here I'm going to show how to run a linear trend, again for one single study, and then how to use the ci.x function in the AP package to interpret the results. In this case we will interpret that every three, every one, cap's increasing, coffee is associated with a 3% increase in the mortality risk. Of course we've been seeing that from the actual data this might not be appropriate, so we can run also a non-linear model, and here I'm using restricted QB spline in the RMS package. And now the output is a little bit more difficult to interpret as the coefficient that don't have a strict interpretation. So we can see that there is an evidence of an association, so this is a p-value tested that both of the coefficients are equal to zero. And then here we see that there is also evidence of a non-linear relationship as dictated by this p-value. So how to interpret the results? Then we can predict those in terms of predictive renter risk, and now we see that there is a better agreement with what we'd expect. Now adding this, so we were able to estimate the dose response association based on publishers that's from one studies. What happened when we have multiple studies? So basically I'm expanding what I did before to just display the data that we want to model now. And by applying the same two models to all the studies, then we are able to also get the same prediction for all the studies. I'm not focusing on the code here, but you can copy and paste to reproduce it. And then you can see that there is some variation in the observed results, but a tendency in an inverse association which might not be linear in most of the studies. So how can we summarize this evidence? Then we are doing a meta-analysis. So basically we are taking all the coefficients which are which specify the dose response association, so the beta coefficient that you were seeing in the output before, and then we are running meta-analysis to combine those coefficients. Here I'm just reporting formulas for the univariate case, the linear trend, but then we can expand those also in the multivariate setting using multivariate meta-analysis. So in general we have the square that is the between study heterogeneity, then we can test if there is evidence of an overall association, and then we also can quantify, test the heterogeneity or quantify the impact of this using different measures. And here just showing how you can do this using the meta-4 package, or in the case of the linear setting, or using the other packages here I'm using the MV meta by Gasparini for pooling multivariate beta coefficient. So having said that, I will cover instead how you can use and why I implemented and released the dose-response meta-package. So the dose-response meta-package facilitates the two different analyses, so both the dose-response analysis and the pooling analysis, so you don't have to implement yourself or using different packages. So in such a way you'll get a most comprehensive framework for the two analysis altogether. And then of course there are additional functions to ease different tasks of the meta-analysis such as testing, predicting and interpreting, and meaning that presenting also the results. And then I also implement a set of extensions to the basic methodology. So I'll just show you how to do in two lines what I did before in several steps. So now with the function dose-response meta, if I specify the ID arguments, specify different studies, then I'm able to estimate an overall linear trend. And again if you want to interpret you can put on a lot, you can exponentiate the coefficient and then interpret as an overall 3% decrease in mortality risk. If we are not satisfied with a linear model, then we can turn to the non-linear model. Different options are available. I also have some code for fractional polynomials, other non-linear models like a log exposure model. Here I'm using again for comparability as with the previous example, the restricted QB spline. And again here you can test if there is an overall association, you can look in the Q test and here you're going to have evidence of a significant residual heterogeneity and then you can quantify the impact of this heterogeneity to be around 60%. How to present the results? We can use the predict function implemented for predicting on a new data here that is specified and just putting a zero at the beginning. So this is going to be my reference and the values are presented on an exponential scale since this is our unit of interpretation. And then we can see that there is an overall non-linear association with the lowest or highest decrease in mortality risk between 3 and 4 caps per day as discussed in the paper. So from this we can do more, of course. We can try to predict the results of a future study or try to predict the results on the individual studies using the Bloop, the best linear and biased estimator prediction. And so in such a way we use the normality assumption on the random effects to get a better prediction of the individual curves. And I left here the formulas for the linear, so the univariate case but then I also presented some of the more, slightly more complicated codes to get the actual curves. And you see that here as a dotted line I'm presenting the Bloop and I compare to the individual curves that I was presenting before. And you see that somehow these curves are more close to the average than the individual curves using some of the information that we've been gaining from the model. Just briefly sketching some of the addition capabilities here. We've been discussing, implementing and publishing how to evaluate the goodness of it using different measures, the deviance test, the R-square as a coefficient of determination or using a plot as of the decorrelative receivial to better evaluate the agreement of the model. You see here we're using the function GOF, how to get this quantity and how to get a plot to investigate the potential influence of some of the points. And of course there are more to do in the meta-analysis here and just presenting the meta-regression or stratified analysis to try to explain some of the residuality originate in the model and this has of course some advantages because it gets more knowledge over new results but of course it gets a little bit complicated by the limited number of data points and this is by the limited number of studies, it's not the those data points that make a difference. So I can show you here how we want to explain the residuality originate using the extra argument, more mod as a function of the geographical area and then we can of course use the whole test function to test this hypothesis. And we see that they're my some indication of differences of those response association between different geographical area and again if we want to present this data we see that the American they have a lower mortality reduction as compared for example to Europe and then we see a really strange curve for Japan. If we look more into this we see that this is actually explained but a very narrower exposure range so limiting to up to three or four cups per day as a maximum observed range in that studies. And just to conclude that we'll just catch a few model extension one I was covering it was the one stage procedure so this is a more comprehensive model strategies is equivalent to the two stage procedure when we have the same available data but of course the one stage is a more general framework is conceptually easier, can fit more elaborate curves and avoid the exclusion of studies with limited data points. So I didn't specify that before but when we estimate that those response model we actually are required that each studies are providing at least the same number of non-referent doses as the number of parameters that we're estimating. So basically those studies presenting only one non-referent relative risk will be excluded from a non-linear analysis. This is not the case from the one stage procedure and here I'm just showing using the additional data in the R dose of res meta package how we can add some more data that got excluded in the main analysis and how to estimate the actually those response model using in a one stage procedure by specifying proc equal to one stage. So here is how the two results change. They don't change a lot but we see that with the one stage we have even a further reduction in the predicted curve. The second extension that I'm covering is the application of this dose response methodology in the case of drug pharmaceutical studies where the outcome is not a log relative risk but is usually expressed in terms of means or difference in means. Have a look at the paper and contact me if you have any questions. And I will conclude with some references and codes here on the main webpage. You can see some reproducible code that the article had been published, some analysis example and additional useful code for tackling some particular aspects you might be interested in. I also have a look at my GitHub repository where I have also the package and some of the presentation and additional material. Some of the slides that I've been presenting and the user in 2016, this is a little bit of update of those an extension of those slides. And then if you're interested in playing around I also develop a shiny app. So you can have a look at that as well. And then some of the articles that I've been covering the packaging, the journal statistical software, the additional methodology, one stage methodology or those response method analysis of differences in mean and the original article where I published the results of this applied, those response method analysis. Feel free to contact me if you have any question or find any mark in the package. I hope this can be helpful for you. Thank you for listening.